Someone listed all the numbers from 0 to 99999 in increasing order. Then he crossed out all the numbers where some other digit (s) besides 0 and 1 were used.

Answer: 32

Step-by-step explanation:

Write out all numbers between 0 and 99,999 that * only * contain the number zero and/or number 1.

1. 0

2. 1

3. 10

4. 11

5. 100

And so on, until you get to ...

32. 11,111

Step-by-step explanation:

Lets write all the possible numbers.

One digit: 0,1

Two digits: 10, 11

Three digits: 100, 101, 110,111

Four digits: 1000,1001, 1010, 1011, 1100, 1101, 1110, 1111

Five digits: 10000,10001,10010,10011,10100, 10101, 10110,10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110,11111.

The other numbers of the list must be crossed.